Rigid body objects converted to mesh from a particle system don't get simulated
If I understand correctly, you have originally assigned Rigid Body properties to your "reference" cube (the one that got duplicated by the particle system).

Even though this effectively assigns the Rigid Body properties to the child objects, it doesn't automatically add them to the RigidBodyWorld group, that is the group that the physics engine takes into consideration when baking dynamics (unless otherwise specified in the rigid body settings).

You can see that they are not part of a group by observing that their wireframe is not colored green. 

There is a quick fix to this: select all your boxes and hit "Add active" in the "Physics" panel of the toolbox to the left of the 3D window.